Representações aditivas em grupos abelianos finitos

Abstract

In this work, we will present some forms to write the elements of a given abelian group G as element of sum sets or as element of sum of the terms of one given sequence. We will show several types of direct problems, for instance, the Theorem of Cauchy- Davenport and Theorem of Chowla, and inverse problems as the Theorem of Vosper. The representation of a element as sum of terms of a sequence appears with the Theorem of Erd¨os-Ginzburg-Ziv. From the theorem of Mann, a sequence of length 2p - 1 in Zp represents at least one time every element of this group. Thus the Theorem of Gao, may be considered as a refinement of the Theorem of Mann. By using Davenport constant, lower bound on the length of a sequence such that it represents the identity element of the group is investigated, mainly it is studied in the group formed for d copies of Zn